The prison experiment is generally not reenacted. It was hideously poorly designed to start with and the results weren't even clearly interpretable in a useful fashion. Milgram type fake electric shock experiments can still be done (although some people have argued that they are unethical). I don't know if this sort of thing has been tested for in those experiments, but I'd predict that you would actually not get a substantial result of this sort. The reasoning behind my prediction is that child rearing has become less obedience driven in the US in the last few years but the breakdown of proportions willing to shock people to (and to what extent) has remained roughly constant since Milgram's initial experiments. If parenting forms matter we'd expect to see a decline in the fraction of people willing to severely shock in Milgram set-ups.

Edit: Thinking about this slightly more. We'd need to be careful about the exact experimental setup since going through with a Milgram electric shock experiment might make people answer questions about morality and upbringing differently than if they had not. But there's also the problem that asking people such questions before hand might alter behavior as well. So there really should be three groups tested: A standard Milgram set-up, a set where they are asked the relevant questions before hand, and a set where they are asked afterwords. If we see a lot of difference in how the two groups asked about their moral upbringings respond then that would suggest that the Oliner study isn't reliable.